

A330218


Least BIInumber of a setsystem with n distinct representatives obtainable by permuting the vertices.


6




OFFSET

1,2


COMMENTS

A setsystem is a finite set of finite nonempty sets of positive integers.
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem has a different BIInumber. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BIInumber of {{2},{1,3}} is 18. Elements of a setsystem are sometimes called edges.


LINKS

Table of n, a(n) for n=1..6.


EXAMPLE

The sequence of setsystems together with their BIInumbers begins:
0: {}
5: {{1},{1,2}}
12: {{1,2},{3}}
180: {{1,2},{1,3},{2,3},{4}}
35636: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{5}}
13: {{1},{1,2},{3}}


MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Apply[Rule, Table[{p[[i]], i}, {i, Length[p]}], {1}])], {p, Permutations[Union@@m]}]];
dv=Table[Length[graprms[bpe/@bpe[n]]], {n, 0, 1000}];
Table[Position[dv, i][[1, 1]]1, {i, First[Split[Union[dv], #1+1==#2&]]}]


CROSSREFS

Positions of first appearances in A330231.
The MMnumber version is A330230.
Achiral setsystems are counted by A083323.
BIInumbers of fully chiral setsystems are A330226.
Cf. A000120, A003238, A007716, A016031, A048793, A055621, A070939, A214577, A326031, A326702, A330098, A330101, A330195, A330217, A330229, A330233.
Sequence in context: A332466 A323565 A195538 * A047658 A290804 A353365
Adjacent sequences: A330215 A330216 A330217 * A330219 A330220 A330221


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 09 2019


STATUS

approved



